Line Mixing Effects Research Articles

Measurements of air-broadened width and air-induced shift coefficients and line mixing in the ν6 band of 12CH 3D

Air-broadening and shift coefficients for more than 680 transitions in the 1040– 1410 cm −1 spectral region of the ν 6 perpendicular band of 12CH 3D have been measured. Values have been obtained from analysis of 11 room temperature absorption spectra recorded at 0.005 cm −1 resolution with the McMath–Pierce Fourier transform spectrometer located on Kitt Peak National Solar Observatory and retrieved using a multispectrum nonlinear least-squares fitting technique. The measured broadening coefficients range from 0.016 to 0.077 cm −1 atm −1 at 296 K for transitions up to J″=17 and K″=15, including 34 forbidden lines with 2≤Δ K≤4. The corresponding pressure-induced shift coefficients vary from −0.012 to +0.008 cm −1 atm −1 , and the majority of these are negative. Within each J series in the P P and R R sub-bands, the J″= K″ (and J′= K′) transition exhibited the smallest broadening coefficient. In the P Q sub-band, the J″= K″ transition in each J series of lines had the largest positive pressure-shift coefficient while the largest negative pressure-shift coefficients were associated with the J′= K′ lines in the R Q sub-band. Subsets of the air-broadened width coefficients vary somewhat smoothly as a function of the rotational quanta, and this behavior has been modeled to ±8% using empirical expressions. Finally, Line mixing effects were observed for the first time in several of the K″=3 ( A + A −) split components in the PP, PQ, PR, RP, RQ and R R sub-band transitions, and values for off-diagonal relaxation matrix coefficients were determined.

Measurements of air broadening, pressure shifting and off diagonal relaxation matrix coefficients in the ν3 band of 12CH3D

A multispectrum nonlinear least-squares fitting technique has been applied to determine Lorentz air-broadening coefficients and air induced pressure-shift coefficients of 12CH3D for the ν3 fundamental band in the spectral region between 1154 and 1430cm−1. This analysis has utilized 11 absorption spectra recorded at an unapodized resolution of 0.005cm−1 with the McMath-Pierce Fourier transform spectrometer of the National Solar Observatory (NSO) on Kitt Peak. Low pressure spectra (with 1–2.99Torr of enriched 12CH3D samples) as well as lean mixtures (≈1%) of 12CH3D in dry air (total pressures of 100–400Torr) at room temperature have been measured to determine the pressure broadening coefficients of more than 360 ν3 transitions with quantum numbers as high as J″=17 and K″=17. The measured air-broadening coefficients range from 0.0155 to 0.0726cm−1atm−1 at 296K. The pressure-induced shift coefficients vary from about −0.0086 to +0.0058cm−1atm−1. The majority of the shifts are negative, and the positive shifts often involve transitions with J″=K″. Weak line mixing effects have also been observed in a few high J lines with K″=3 and approximate off diagonal relaxation matrix coefficients were determined for several A+A− (A1A2) split components. At low to medium values of J, the A+A− splitting is extremely small, and the two components are practically unresolved. Variations of the measured parameters with the A- and E- symmetry species and the rotational quantum numbers of the transitions involved are discussed. The present results are compared to the few available experimental values in the literature.

Air- and N2-Broadening Parameters of HDO and D2O, 709 to 1936 cm−1

High-resolution measurements of air- and N2-broadened widths and pressure-induced frequency shifts of HDO and D2O covering the spectral region between 700 and 2000 cm−1 were obtained with absorption paths of 2.39, 25, 73, and 193 m. The majority of the measurements included the (010)–(000) bands of HD16O and D216O. Also measured were 17 lines of the pure rotational band of HD16O and several transitions of the (010)–(000) bands of HD18O and D218O and a few transitions of the “hot” band, (020)–(010), for HD16O and D216O. The observed width coefficients ranged from 0.02 to 0.1 cm−1/atm and the pressure-induced shift coefficients fell between +0.012 and −0.012 cm−1/atm. Line mixing was observed for a few of the pairs of transitions of HDO but was of no consequence for D2O lines. However, the effects of line mixing were small and accurate results were obtained using the Voigt line profile. Collisional narrowing effects were not observed in the data.

Experimental and theoretical study of line mixing in methane spectra. II. Influence of the collision partner (He and Ar) in the v3 IR band

Line mixing effects are studied in the v3 band of CH4 perturbed by Ar and He at room temperature. Experiments have been made in the 2800–3200 cm−1 spectral region using four different setups. They cover a wide range of total densities, including low (0.25–2 atm), medium (25–100 atm), and high (200–1000 atm) pressure conditions. Analysis of the spectra demonstrates that the spectral shapes (of the band, the Q branch, the P and R manifolds,…) are significantly influenced by line mixing. The theoretical approach proposed in the preceding paper is used in order to model and analyze these effects. As done previously, semiclassical state-to-state rates are used together with a few empirical constants. Comparisons between measurements and spectra computed with and without the inclusion of line mixing are made. They prove the quality of the approach which satisfactorily accounts for the effects of pressure and of rotational quantum numbers on the spectral shape. It is shown that collisions with He and Ar lead to different line-coupling schemes (e.g., more coupling within the branches and less between branches) and hence to different shapes. The influence of line coupling between different branches and manifolds is evidenced and studied using high pressure spectra and absorption in the band wings.

Model, software, and database for computation of line-mixing effects in infrared Q branches of atmospheric CO 2: II Minor and asymmetric isotopomers

The influence of line-mixing on the shape of infrared Q branches of minor isotopomers of CO 2 is studied for the first time. Laboratory spectra of isotopically enriched CO 2–N 2 mixtures have been measured in the 15 μm region at the temperatures of 200 and 300 K for total pressures between 1 and 10 atm. Comparisons with measurements for the ν 2 and ( ν 1– ν 2) I Q branches of the six isotopomers (16, 17, or 18) O- 12C–O (16, 17, or 18) demonstrate the quality of the theoretical approach presented in the preceding paper (Part I). The model is used to generate a set of numerical data ( available by ftp) for the prediction of absorption by 16O 12C 18O, 16O 12C 17O, 16O 13C 18O, 16O 13C 17O, and 17O 12C 18O infrared Q branches under atmospheric conditions; this database completes that proposed in the preceding paper and now includes 271 bands considering the eight most abundant CO 2 isotopomers. Its quality is tested by comparisons with atmospheric limb emission measured by a balloon-borne high resolution Fourier transform instrument. The ν 2 Q branches of 16O 12C 16O, 16O 13C 16O, 16O 12C 17O, and 16O 12C 18O recorded above Alaska have been used. This shows that line mixing has significant effects, even for minor isotopomers, and is correctly accounted for by the model and data proposed.

Experimental and theoretical study of line mixing in methane spectra. I. The N2-broadened ν3 band at room temperature

Line-mixing effects have been studied in the ν3 band of CH4 perturbed by N2 at room temperature. New measurements have been made and a model is proposed which is not, for the first time, strictly empirical. Three different experimental set ups have been used in order to measure absorption in the 2800–3200 cm−1 spectral region for total pressures in the 0.25–2 and 25–80 atm ranges. Analysis of the spectra demonstrates the significant influence of line mixing on the shape of the Q branch and of the P and R manifolds. A model is proposed which is based on state-to-state collisional transfer rates calculated from the intermolecular potential surface with a semiclassical approach. The line-coupling relaxation matrix is constructed from these data and two additional parameters which are fitted on measured absorption. Comparisons between measurements and spectra computed accounting for and neglecting line mixing are made. They prove the quality of the approach which satisfactory accounts for the effects of pressure and of rotational quantum numbers on the spectral shape under conditions where modifications introduced by line mixing are important. For high rotational quantum number lines, the main features induced by collisions are predicted but some discrepancies remain; the latter may be due to improper line-coupling elements but there is strong evidence that the use of inaccurate line broadening parameters also contributes to errors in calculated spectra.

Temperature, pressure, and perturber dependencies of line-mixing effects in CO2 infrared spectra. III. Second order rotational angular momentum relaxation and Coriolis effects in Π←Σ bands

The energy corrected sudden approach is used in order to deduce collisional parameters and to model infrared quantities in Π←Σ bands of CO2–He and CO2–Ar mixtures in the 200–300 K temperature range. Measured line-broadening coefficients and absorption in the Q-branch of the ν2 band at moderate pressure are first used for the determination (from a fit) of the time constant associated with the relaxation of the second order traceless tensor of the rotational angular momentum (all other collisional quantities have been determined previously). The results obtained are consistent with previous (calculated) temperature dependent values of the depolarized Rayleigh cross sections. The model is then successfully tested through computations of absorption in the ν2 and (ν1+ν2)I bands at elevated densities. Analysis of line-mixing effects is made, including study of the influence of interbranch transfers and of Coriolis coupling. Differences between the effects of collisions with He and Ar are pointed out and explained.

Experimental and theoretical study of the far-infrared spectra of HCl dissolved in liquid Ar, Kr, and Xe

New experimental results are reported on the relative absorption intensity distribution in the FIR spectra of HCl dissolved in liquefied Ar, Kr, and Xe at several temperatures along the liquid—vapour coexistence curve. These are treated further by applying a previously developed quantum-statistical spectral theory, which accounts for the line mixing and memory effects. Theoretical spectra are given in terms of the anisotropic potential time autocorrelation functions obtained from classical MD simulations using several empirical analytical potentials with density-adjusted well depths. Globally fair agreement between the theoretical and experimental spectra is demonstrated, except in the high frequency wings, where the theory underestimates the observed intensities. The choice of a particular radial form for the anisotropic HCl/RG potentials is found to be not critical for reproducing the experimental absorption profiles.

Experimental and theoretical study of the far-infrared spectra of HCl dissolved in liquid Ar, Kr, and Xe

New experimental results are reported on the relative absorption intensity distribution in the FIR spectra of HCl dissolved in liquefied Ar, Kr, and Xe at several temperatures along the liquid—vapour coexistence curve. These are treated further by applying a previously developed quantum-statistical spectral theory, which accounts for the line mixing and memory effects. Theoretical spectra are given in terms of the anisotropic potential time autocorrelation functions obtained from classical MD simulations using several empirical analytical potentials with density-adjusted well depths. Globally fair agreement between the theoretical and experimental spectra is demonstrated, except in the high frequency wings, where the theory underestimates the observed intensities. The choice of a particular radial form for the anisotropic HCl/RG potentials is found to be not critical for reproducing the experimental absorption profiles.

MODEL, SOFTWARE, AND DATABASE FOR COMPUTATION OF LINE-MIXING EFFECTS IN INFRARED Q BRANCHES OF ATMOSPHERIC CO 2—I. SYMMETRIC ISOTOPOMERS

A theoretical model based on the energy-corrected sudden approximation is used in order to account for line-mixing effects in infrared Q branches of symmetric isotopomers of CO 2. Its performance is demonstrated by comparisons with a large number (about 130) of CO 2–N 2 and CO 2–O 2 laboratory spectra recorded by several instrument setup: nine Q branches of different vibrational symmetries lying between 4 and 17 μm are investigated in wide ranges of pressure (0.05–10 atm) and temperature (200–300 K). The model is used to generate a set of suitable parameters and FORTRAN software (available by ftp) for the calculation of the absorption within 12C 16O 2, 13C 16O 2, and 12C 18O 2 infrared Q branches under atmospheric conditions, which can be easily included in existing radiance/transmission computer codes. Comparisons are made between many (about 280) computed atmospheric spectra and values measured using two different balloon-borne high-resolution Fourier transform instruments: transmission (solar occultation) as well as radiance (limb emission) measurements of seven Q branches between 12 and 17 μm for a large range of atmospheric air masses and pressure/temperature conditions have been used, including the ν 2 band of both 12C 16O 2 and 13C 16O 2. The results confirm the need to account for the effects of line-mixing and demonstrate the capability of the model to represent accurately the absorption in regions which are often used for temperature/pressure sounding of the atmosphere by space instruments. Finally, quantitative criteria assessing the validity of the widely used Rosenkranz first-order approximation are given.

Line-mixing effects in N2O Q branches: Model, laboratory, and atmospheric spectra

A model based on the energy corrected sudden approximation is used in order to account for line-mixing effects in N2O Q branches of Σ↔Π bands. The performance of this theoretical approach is demonstrated by comparisons with many (about 70) N2O–N2 and N2O–O2 laboratory spectra recorded in the 5 and 17 μm regions by three instrument setups; the Q branches of the 2ν20e–ν21f (near 579.3 cm−1), ν2 (near 588.8 cm−1), and ν2+ν3 (near 2798.3 cm−1) bands are investigated for different pressures (0.1–2.0 atm) and temperatures (200–300 K). The model is used to generate a set of line-mixing parameters for the calculation of the absorption by the ν2 Q branch under atmospheric conditions. These data are tested by comparisons between computed stratospheric emissions and values measured using a balloon-borne high resolution Fourier transform instrument. The results confirm the need to account for the effects of line mixing and demonstrate the capability of the model to represent the N2O absorption in a region which can be used for the retrieval of N2O5 mixing ratios.

Double scattering on the nucleus in the perturbative QCD

Line mixing effects have been studied in the band of perturbed by helium. Theoretical absorption coefficients are compared to FTIR measurements, which were made at room temperature for helium pressure from 1 atm up to 90 atm. The observed strong modifications with respect to additive Lorentzian contributions are explained by line coupling effects. The Infinite Order Sudden Approximation and the Energy Corrected Sudden Approximation are used in order to account for these effects. The latter gives better agreement: it rather successfully predicts the band shape and the linewidths.

Line-mixing effects in He- and N2-broadened Σ↔Π infrared Q branches of N2O

Two Q branches of N2O near 579.3 and 2798 cm−1 belonging to the 2ν20e−ν21f and ν2+ν3 bands, respectively, of Σ←Π and Π←Σ symmetry, have been studied for He and N2 perturbers at pressures ranging from 0.1 to 2 atm, using a tunable diode laser and a difference-frequency laser spectrometer. To interpret the line-mixing effects in these spectra, we have applied a model based on the energy corrected sudden approximation whose parameters have been only derived from line-broadening data for N2O–He and also from the measured absorption by the Q branches for N2O–N2. This model provides a satisfactory agreement with experimental band shapes, whatever the band, the perturber and the pressure considered. Significantly larger line-mixing effects are shown for N2O–He with respect to N2O–N2. Finally, the assumption made in the calculations to treat separately the couplings in the even and odd j levels appears to have a negligible influence on the resulting band shapes.

Temperature, pressure, and perturber dependencies of line-mixing effects in CO2 infrared spectra. II. Rotational angular momentum relaxation and spectral shift in Σ←Σ bands

The Energy Corrected Sudden approach is used in order to deduce collisional parameters and to model infrared quantities in Σ-Σ bands of CO2-He and CO2-Ar mixtures at room temperature. Measurements are first used for the determination (from a fit) of the rotational angular momentum relaxation time and of some parameters representative of the imaginary part of the relaxation operator. It is shown that line-broadening data as well as absorption in both the wing and central part of the ν3 and 3ν3 bands lead to consistent determinations. The model is then used for detailed analysis of line-mixing effects. The influences of pressure, of the band spectral structure, and of the collision partner are studied. Differences between the effects of collisions with He and Ar are pointed out and explained.

Diode-laser measurements of He- and N 2-broadening coefficients and line-mixing effects in the Q-branch of the ν1– ν2 band of CO 2

He- and N 2-broadening coefficients have been measured for the lines Q2 to Q22 of the v 1- v 2 (10 001 ← 01 101) band of CO 2 near 720.80 cm −1, using a tunable diode-laser spectrometer. The collisional widths have been obtained at low perturber pressures by fitting Voigt and Galatry profiles to the measured shapes of the lines. Spectra in the v 1- v 2 band of CO 2 in mixture with He and N 2 have also been recorded at higher pressures. The deviations observed from an additive superposition of Lorentzian lines have been notably reduced by considering collision-induced line-mixing effects.

Kinetic theory of band shapes in molecular spectra of gases: Application to band wings

A kinetic theory of spectral band shapes is developed which accounts for the effects of line mixing and finite duration of collisions. The theory is based on a projection operator technique with a nonorthogonal metric. The roles and hierarchy of various approximations commonly employed are analyzed. It is shown that the relaxation operator must be defined before the initial correlations are suppressed so that the double sum rule for the matrix elements of this operator is conserved. This conservation is important for the calculations of the wings of band shapes. Rotovibrational band shapes for some specific cases of Raman and infrared absorption spectra of gases are considered. The expressions obtained relate the band wing profiles with the spectral density of molecular torque arising from binary collisions.

Line-Mixing Effects inQBranches of CO2

A theoretical model based on the energy corrected sudden (ECS) approximation is used in order to account for line-mixing effects in Δ ↔ Π infraredQbranches of12C16O2. Its quality is demonstrated by comparisons with numerous laboratory spectra of CO2–He and CO2–N2mixtures: threeQbranches in the 4 and 17 μm regions are investigated at room temperature in a wide pressure range. The influence of mixing betweenQ(J) lines associated with odd and even values of the rotational quantum numberJis demonstrated and analyzed in detail. It is shown that, in contrast to available fitting law approaches, the ECS model correctly predicts the influence of the parity of the rotational quantum numbersJandJ′ on coupling between theQ(J) andQ(J′) lines. Comparisons between the effects of collisions of CO2with N2and He are made and analyzed. They show that these two systems involve different line couplings within theQbranch.

Line-Mixing Effects inQBranches of CO2

A theoretical model based on the energy corrected sudden (ECS) approximation is used to account for line-mixing effects in infraredQbranches of parallel bands of CO2. Measurements have been made using a tunable difference frequency spectrometer system in a Π–Π transition: spectra of the 1111II← 0110IQbranch near 3580.3 cm−1have been recorded at room temperature for CO2–He and CO2–N2mixtures in the 0.1–1 atm total pressure range. Comparisons of experimental and computed spectra prove the quality of the ECS approach. It is shown that the influence of line mixing on the shape of parallelQbranches is very weak and much smaller than in perpendicular transitions. This result is analyzed in detail and explained in terms of the effects of the vibrational angular momenta on the dipole transition moments and vector coupling coefficients involved in the relaxation operator elements. The effects of collisions of CO2with N2and He are compared and discussed.

Interbranch line-mixing in CO2 (101) and (021) combination bands

Absorption spectra from a mixture of 320 ppm CO2 in synthetic air (79% N2, 21% O2) were collected in the region from 3500 cm−1 to 4000 cm−1 under conditions in the range of 100–1000 atm and 295–900 K. At 295 K, both bands of the (1001), (0201) Fermi dyad show the collapse of P and R branches into a single nearly Lorentzian spectral feature as a result of interbranch line-mixing. At elevated temperatures, the presence of interbranch mixing is also clearly evident as is the presence of several hot bands. The experimental data are modeled using two methods for simulating line-mixed spectra; first, the usual line-by-line approach which relies on the binary impact approximation, and second, a simple band-averaged model proposed by Hartmann and L’Haridon [J. Chem. Phys. 103, 6467 (1995)]. The energy corrected sudden (ECS) approximation is used to generate the relaxation matrix in the first approach. Comparison with the measurement shows that the ECS method does not fit the high density data satisfactorily when adjustable parameters from the literature are used; the level of interbranch mixing must be decreased by about a factor of 2 relative to intrabranch mixing and at least 5% dephasing must be added to the ECS matrix. With these changes, the room temperature data are modeled satisfactorily, but significant discrepancies are still present in the high temperature spectra. On the other hand, the simpler band-averaged model does provide a reasonable estimate of the spectra for all temperatures when best fit values are used for mixing and broadening, but the low density data are not reproduced as well as with the ECS model. Data from high pressure absorption measurements in a 1% NO in N2 mixture as well as a 0.5% CH4 in N2 mixture are also presented without analysis, showing the effects of interbranch line-mixing in these spectra.

Temperature, pressure, and perturber dependencies of line-mixing effects in CO2 infrared spectra. I. Σ←Π Q branches

Experimental and theoretical results on the influence of line mixing on the shape of infrared CO2 Q branches of importance for atmospheric applications are presented. Two Q branches of Σ←Π symmetry, which lie near 618 and 720 cm−1 and belong to the 1000II←0110I and 1000I←0110I bands, have been studied for many conditions of temperature (200–300 K), total pressure (0.5–10 atm), and mixture (with He, Ar, O2, and N2). The theoretical approach used is based on the Energy Corrected Sudden approximation; its parameters have been deduced from both line-broadening data and measured absorption by the Q branches. Comparisons between experimental and computed spectra demonstrate the quality of the model, regardless of the conditions. Detailed analysis of the influences of the Q-lines spectral spacing, temperature, total pressure, and collision partner are presented. They show that significantly larger line-mixing effects are obtained when CO2–He is considered with respect to CO2–(Ar,O2,N2). This is analyzed in terms of the relative contributions of the short- and midrange interaction forces and of propensity rules resulting from the coupling of angular momenta.